Starting with polynomial:
P : 16*t^4 - 48*t^2 + 12
Extension levels are: 4 45
-------------------------------------------------
Trying to find an order 45 Kronrod extension for:
P1 : 16*t^4 - 48*t^2 + 12
Solvable: 1
-------------------------------------------------
Ending with final polynomial:
P : 16*t^49 - 1537941489400837442117679296021997144/177036531294596661352651300338773*t^47 + 15683929370310663266474903400854997806856/7258497783078463115458703313889693*t^45 - 2373405748325946181313829135848806992519390/7258497783078463115458703313889693*t^43 + 34965454477640133000074576736527867030969970/1036928254725494730779814759127099*t^41 - 127247659754142243730128142495189565478602655/50581866084170474672186085811078*t^39 + 7116205621387214994851294254910534685293059515/50581866084170474672186085811078*t^37 - 1220198608672994909977428334590228588078095557515/202327464336681898688744343244312*t^35 + 81324391553517566590936800966531494909763308536725/404654928673363797377488686488624*t^33 - 2124568164607482607162736332145284812340596454353225/404654928673363797377488686488624*t^31 + 43691973539551796169511744876281284419907172960499575/404654928673363797377488686488624*t^29 - 2830966114140668649459096205578035482497079636479552525/1618619714693455189509954745954496*t^27 + 36027965030209895797157375308669328449766833984688499975/1618619714693455189509954745954496*t^25 - 1432832966134547034008533448589930869499692703907087404375/6474478858773820758039818983817984*t^23 + 11031826093249543929902840193042562739380098315333601929375/6474478858773820758039818983817984*t^21 - 259848946812676043761553194263202667748015757674521244931875/25897915435095283032159275935271936*t^19 + 4603751540668158721607946838813222071680194616838732863998125/103591661740381132128637103741087744*t^17 - 30007910595611815205288734318782151561744497850917476123750625/207183323480762264257274207482175488*t^15 + 69906272087654449359794802211190611686973592156984086512721875/207183323480762264257274207482175488*t^13 - 448052262212855383779882714893668301507279472013641326525653125/828733293923049057029096829928701952*t^11 + 468689948889818127817321945530430425309574922843690805022790625/828733293923049057029096829928701952*t^9 - 1189917545610040054649328395141714403404856090350855364239971875/3314933175692196228116387319714807808*t^7 + 411021599370556609740330396223368122655873138345844667914434375/3314933175692196228116387319714807808*t^5 - 3261050198515998960740257038511926601880901339443975128640625/167844717756566897626146193403281408*t^3 + 24309741925743407605982199737485515009888509581513105291546875/26519465405537569824931098557718462464*t
-------------------------------------------------
Computing nodes and weights
  current precision for roots: 53
  current precision for roots: 106
 current precision for weights: 53
Linear system for weights solvable: 0
  current precision for roots: 106
  current precision for roots: 212
 current precision for weights: 106
Linear system for weights solvable: 0
  current precision for roots: 212
  current precision for roots: 424
 current precision for weights: 212
Linear system for weights solvable: 1
  current precision for roots: 424
  current precision for roots: 848
 current precision for weights: 424
Linear system for weights solvable: 1
Sufficient bits for target precision reached
Positive weights:   49 out of 49
Indefinite weights: 0 out of 49
Negative weights:   0 out of 49
Extension rule has valid weights: 1
-------------------------------------------------
The nodes are:
| (-6.7029001629600822018 + 1.6068211489943088163e-854j)  +/-  (4.34e-244, 4.34e-244j)
| (5.8609433424828900814 + 1.3420475287283542524e-852j)  +/-  (9.83e-244, 9.83e-244j)
| (8.8753630079815764628 - 4.890991030020446758e-861j)  +/-  (6.99e-247, 6.99e-247j)
| (-3.3009813103405057463 + 3.4691587574313208739e-859j)  +/-  (1.53e-245, 1.53e-245j)
| (-8.8753630079815764628 - 2.1023941521493886495e-861j)  +/-  (6.55e-247, 6.55e-247j)
| (7.1604631570506002787 - 9.6333906488943288227e-859j)  +/-  (2.19e-244, 2.19e-244j)
| (3.3009813103405057463 + 5.464096066477728272e-858j)  +/-  (1.58e-245, 1.58e-245j)
| (8.2086711523895688967 + 4.9117123268816322402e-860j)  +/-  (9.19e-246, 9.19e-246j)
| (7.6553882566409289929 - 1.1245423263430335596e-858j)  +/-  (5.29e-245, 5.29e-245j)
| (3.6443140100218668114 + 3.5838719198521208618e-857j)  +/-  (5e-245, 5e-245j)
| (2.298532145874190896 + 1.1954552161725588762e-863j)  +/-  (2.1e-247, 2.1e-247j)
| (-2.298532145874190896 + 8.128864808992047359e-864j)  +/-  (1.96e-247, 1.96e-247j)
| (4.3486636422167737537 + 6.5741825393555740563e-860j)  +/-  (2.89e-244, 2.89e-244j)
| (2.9625657833773618123 + 5.3719524065902318048e-865j)  +/-  (4.38e-246, 4.38e-246j)
| (6.7029001629600822018 - 2.2089988313940350308e-861j)  +/-  (4.45e-244, 4.45e-244j)
| (1.3347572563713197439 + 8.8029792971729652027e-875j)  +/-  (6.13e-250, 6.13e-250j)
| (-8.2086711523895688967 + 5.3408739052360431951e-871j)  +/-  (9.87e-246, 9.87e-246j)
| (-3.6443140100218668114 - 3.9279155409603991525e-868j)  +/-  (4.72e-245, 4.72e-245j)
| (-2.6285347521674731702 - 3.9370561761862878278e-872j)  +/-  (1.03e-246, 1.03e-246j)
| (-4.7116069242374598881 - 4.9580428584730119004e-869j)  +/-  (5.35e-244, 5.35e-244j)
| (-6.271888478865773581 + 6.8283088640256684083e-871j)  +/-  (7.56e-244, 7.56e-244j)
| (6.271888478865773581 - 1.2918658379880873055e-871j)  +/-  (7.89e-244, 7.89e-244j)
| (-7.1604631570506002787 + 3.0217469225045721778e-884j)  +/-  (1.83e-244, 1.83e-244j)
| (-1.9724553277714874514 - 1.9399653689749063888e-893j)  +/-  (3.37e-248, 3.37e-248j)
| (5.4657888538689545546 + 2.8329594144874104289e-889j)  +/-  (1.03e-243, 1.03e-243j)
| (-7.6553882566409289929 - 1.321929729625337948e-903j)  +/-  (5.54e-245, 5.54e-245j)
| (3.9932545840061727517 + 1.0879738512481053762e-902j)  +/-  (1.31e-244, 1.31e-244j)
| (2.6285347521674731702 - 7.7658478644901837422e-907j)  +/-  (1e-246, 1e-246j)
| (-1.6506801238857845559 + 4.1748232589423847967e-908j)  +/-  (4.75e-249, 4.75e-249j)
| (-1.0299258554105005784 - 1.1025350422016418123e-909j)  +/-  (7.27e-251, 7.27e-251j)
| (-5.4657888538689545546 + 5.7814191754574439246e-902j)  +/-  (1.04e-243, 1.04e-243j)
| (-1.3347572563713197439 + 1.1254780047409429075e-915j)  +/-  (5.46e-250, 5.46e-250j)
| (1.9724553277714874514 + 2.5688575285645735852e-914j)  +/-  (3.38e-248, 3.38e-248j)
| (-5.8609433424828900814 - 8.7714461313001403946e-910j)  +/-  (1e-243, 1e-243j)
| (0.52464762327529031788 + 4.6518640402516368102e-930j)  +/-  (1.38e-252, 1.38e-252j)
| (-2.9625657833773618123 - 1.5201722374237938182e-928j)  +/-  (4.23e-246, 4.23e-246j)
| (5.0834164919313342812 - 1.5883432669683964485e-945j)  +/-  (8.98e-244, 8.98e-244j)
| (1.0299258554105005784 + 2.1364114405477443312e-960j)  +/-  (7.64e-251, 7.64e-251j)
| (-5.0834164919313342812 + 8.4318365573766818313e-954j)  +/-  (8.62e-244, 8.62e-244j)
| (-4.3486636422167737537 - 7.7335058584978738173e-958j)  +/-  (2.93e-244, 2.93e-244j)
| (-0.75369818993575768558 - 5.6238628142540062583e-972j)  +/-  (9.73e-252, 9.73e-252j)
| (5.2077232043272039799e-976 - 2.4607723420205172649e-976j)  +/-  (2.82e-974, 2.82e-974j)
| (0.28077392485041085934 + 1.4050894126572252025e-973j)  +/-  (1.2e-253, 1.2e-253j)
| (-3.9932545840061727517 - 1.363902219737277435e-969j)  +/-  (1.31e-244, 1.31e-244j)
| (4.7116069242374598881 - 1.4254603117575196593e-980j)  +/-  (5.46e-244, 5.46e-244j)
| (-0.52464762327529031788 + 2.89091308865264204e-992j)  +/-  (1.34e-252, 1.34e-252j)
| (-0.28077392485041085934 - 9.4357464154464679736e-993j)  +/-  (1.3e-253, 1.3e-253j)
| (1.6506801238857845559 - 1.4311933342342884633e-988j)  +/-  (4.82e-249, 4.82e-249j)
| (0.75369818993575768558 + 4.8873403476731828308e-991j)  +/-  (1.01e-251, 1.01e-251j)
-------------------------------------------------
The weights are:
| (7.6809979059024349017e-21 - 1.4299363173749690753e-871j)  +/-  (1.56e-76, 2.73e-197j)
| (2.7406347688648023884e-16 - 2.2442406681084420891e-867j)  +/-  (4.3e-74, 7.5e-195j)
| (2.674475228359958319e-35 + 1.8614074514606830166e-878j)  +/-  (5.41e-83, 9.43e-204j)
| (3.5613040904494425307e-06 + 2.3424831453123677491e-863j)  +/-  (5.15e-64, 8.98e-185j)
| (2.674475228359958319e-35 - 4.130316060144535186e-879j)  +/-  (1.12e-83, 1.96e-204j)
| (1.4449880318050814315e-23 - 4.698153709010985946e-872j)  +/-  (6.94e-79, 1.21e-199j)
| (3.5613040904494425307e-06 + 1.1548622752056424456e-862j)  +/-  (6.7e-66, 1.17e-186j)
| (1.8290919884439727426e-30 - 7.2287860342549164886e-876j)  +/-  (6.76e-82, 1.18e-202j)
| (1.0349787829284476959e-26 + 8.0822404475425253541e-874j)  +/-  (2.04e-80, 3.55e-201j)
| (3.3314684070619536168e-07 - 7.9533025104680233475e-863j)  +/-  (7.76e-69, 1.35e-189j)
| (0.00093946368096637148523 - 1.8522183073571560513e-861j)  +/-  (1.35e-62, 2.35e-183j)
| (0.00093946368096637148523 - 7.631434933085211683e-862j)  +/-  (1.04e-64, 1.81e-185j)
| (1.2405238448355309884e-09 - 4.229809697895254475e-865j)  +/-  (2.76e-72, 4.81e-193j)
| (2.9257784483368892124e-05 - 2.1142221702270175738e-862j)  +/-  (3.28e-66, 5.72e-187j)
| (7.6809979059024349017e-21 + 1.8734208183938400003e-870j)  +/-  (6.56e-79, 1.14e-199j)
| (0.029621532966743131568 + 2.530800192863320258e-860j)  +/-  (1.95e-57, 3.4e-178j)
| (1.8290919884439727426e-30 + 1.3231978859167759354e-876j)  +/-  (5.56e-88, 9.7e-209j)
| (3.3314684070619536168e-07 - 3.567522115502692541e-864j)  +/-  (3.4e-74, 5.93e-195j)
| (0.00018702714993851075371 + 2.5452670064504076357e-862j)  +/-  (2.57e-69, 4.47e-190j)
| (4.7340771495054329053e-11 + 2.6722368402362207716e-866j)  +/-  (3.08e-79, 5.37e-200j)
| (1.9549764073749221806e-18 + 2.7070278898943564088e-870j)  +/-  (6.27e-84, 1.09e-204j)
| (1.9549764073749221806e-18 - 6.8274029057606489614e-869j)  +/-  (3.13e-81, 5.45e-202j)
| (1.4449880318050814315e-23 + 5.2879164301920554017e-873j)  +/-  (1.99e-86, 3.47e-207j)
| (0.0037357596275115011919 + 2.1602061071988843666e-861j)  +/-  (4.43e-70, 7.72e-191j)
| (2.3235642036955718315e-14 + 9.368425813847647514e-867j)  +/-  (2.39e-80, 4.17e-201j)
| (1.0349787829284476959e-26 - 1.1917766068572622172e-874j)  +/-  (7.03e-88, 1.23e-208j)
| (2.3588036089823954853e-08 - 2.0283301873151176405e-864j)  +/-  (2.2e-76, 3.84e-197j)
| (0.00018702714993851075371 + 6.9276775448551220941e-862j)  +/-  (1.13e-72, 1.97e-193j)
| (0.011809937169940381734 - 5.8308759479260426667e-861j)  +/-  (9.06e-71, 1.58e-191j)
| (0.057659473371696423402 - 4.0202682936126085418e-860j)  +/-  (3.12e-68, 5.44e-189j)
| (2.3235642036955718315e-14 + 4.1518062654397473856e-868j)  +/-  (1.16e-83, 2.02e-204j)
| (0.029621532966743131568 + 1.5341056698851166097e-860j)  +/-  (5.44e-71, 9.48e-192j)
| (0.0037357596275115011919 + 4.5966870971729032113e-861j)  +/-  (2.2e-73, 3.83e-194j)
| (2.7406347688648023884e-16 - 3.7972804212218929694e-869j)  +/-  (1.85e-84, 3.22e-205j)
| (0.095015362750756517083 - 1.8892357129410646228e-859j)  +/-  (1.26e-72, 2.2e-193j)
| (2.9257784483368892124e-05 - 8.2247215352507458801e-863j)  +/-  (2.33e-77, 4.06e-198j)
| (1.2730504144515024616e-12 - 3.7449764628091035132e-866j)  +/-  (1.58e-82, 2.75e-203j)
| (0.057659473371696423402 - 5.897821084991274547e-860j)  +/-  (2.98e-74, 5.2e-195j)
| (1.2730504144515024616e-12 - 3.6625536210486940671e-867j)  +/-  (3.53e-83, 6.16e-204j)
| (1.2405238448355309884e-09 - 1.6401407687396488863e-865j)  +/-  (4.59e-82, 8e-203j)
| (0.080311963460921780325 + 9.6639306463737544124e-860j)  +/-  (1.02e-75, 1.79e-196j)
| (0.16180064120540309745 - 1.7383281886460466869e-859j)  +/-  (5.41e-76, 9.43e-197j)
| (0.13978598210621204096 + 1.9164808151033643196e-859j)  +/-  (6.06e-76, 1.06e-196j)
| (2.3588036089823954853e-08 + 8.5154424504957634206e-865j)  +/-  (2.46e-81, 4.3e-202j)
| (4.7340771495054329053e-11 + 1.5207615860655456826e-865j)  +/-  (2.5e-83, 4.36e-204j)
| (0.095015362750756517083 - 1.556824029058427899e-859j)  +/-  (1.23e-76, 2.15e-197j)
| (0.13978598210621204096 + 1.7283194705435606418e-859j)  +/-  (1.11e-76, 1.94e-197j)
| (0.011809937169940381734 - 1.0895769671667384321e-860j)  +/-  (6.82e-79, 1.2e-199j)
| (0.080311963460921780325 + 1.2772859053332159632e-859j)  +/-  (1.51e-77, 2.56e-198j)
